30 citations · 75 across the 21 of their papers we have counts for
22 papers
Differential operator realization of braid group action on quantum groups
Zhaobing Fan, Jicheng Geng, Shaolong Han
We construct a unique braid group action on modified -Weyl algebra . Under this action, we give a realization of the braid group action on quasi-split qu…
Fundamental Limitations on Communication over a Quantum Network
Junjing Xing, Tianfeng Feng, Zhaobing Fan +4
Entanglement, a fundamental feature of quantum mechanics, has long been recognized as a valuable resource in enabling secure communications and surpassing classical limits. However…
Young wall construction of level-1 highest weight crystals over and
Zhaobing Fan, Shaolong Han, Seok-Jin Kang +1
With the help of path realization and affine energy function, we give a Young wall construction of level-1 highest weight crystals over and $U_{q}(D_{4}…
Crystal bases and canonical bases for quantum Borcherds-Bozec algebras
Zhaobing Fan, Shaolong Han, Seok-Jin Kang +1
Let be the negative half of a quantum Borcherds-Bozec algebra and be the irreducible highest weight module with . I…
Differential operator approach to quantum groups and their oscillator representations
Zhaobing Fan, Jicheng Geng, Shaolong Han
For a quasi-split Satake diagram, we define a modified -Weyl algebra, and show that there is an algebra homomorphism between it and the corresponding quantum group. In o…
Braid group actions of quantum Borcherds-Bozec algebras
Zhaobing Fan, Bolun Tong
In this paper, we construct the Lusztig symmetries for quantum Borcherds-Bozec algebra and its weight module , on which the generators with real…
Global bases for quantum Borcherds-Bozec algebras
Zhaobing Fan, Seok-Jin Kang, Young Rock Kim +1
We provide a construction of global bases for quantum Borcherds-Bozec algebras and their integrable highest weight representations.
Abstract crystals for quantum Borcherds-Bozec algebras
Zhaobing Fan, Seok-Jin Kang, Young Rock Kim +1
In this paper, we develop the theory of abstract crystals for quantum Borcherds-Bozec algebras. Our construction is different from the one given by Bozec. We further prove the crys…
Classical limit of quantum Borcherds-Bozec algebras
Zhaobing Fan, Seok-Jin Kang, Young-Rock Kim +1
Let be a Borcherds-Bozec algebra, be its universal enveloping algebra and be the corresponding quantum Borcherds-Bozec algebr…
Drinfeld double of deformed quantum algebras
Zhaobing Fan, Junjing Xing
We provide a deformation, , of Lusztig algebra . Various quantum algebras in literatures, including half parts of two-parameter quantum algebras, quantu…
Equivariant K-theory approach to -quantum groups
Zhaobing Fan, Haitao Ma, Husileng Xiao
Various constructions for quantum groups have been generalized to -quantum groups. Such generalization is called -program. In this paper, we fill one of parts in th…
Quantum Schur duality of affine type C with three parameters
Zhaobing Fan, Chun-Ju Lai, Yiqiang Li +3
We establish a three-parameter Schur duality between the affine Hecke algebra of type C and a coideal subalgebra of quantum affine . At the equal parameter special…
Affine flag varieties and quantum symmetric pairs, II. Multiplication formula
Zhaobing Fan, Yiqiang Li
We establish a multiplication formula for a tridiagonal standard basis element in the idempotented coideal subalgebras of quantum affine arising from the geometry…
Affine Hecke algebras and quantum symmetric pairs
Zhaobing Fan, Chun-Ju Lai, Yiqiang Li +2
We introduce an affine Schur algebra via the affine Hecke algebra associated to Weyl group of affine type C. We establish multiplication formulas on the affine Hecke algebra and af…
Affine flag varieties and quantum symmetric pairs
Zhaobing Fan, Chun-Ju Lai, Yiqiang Li +2
The quantum groups of finite and affine type admit geometric realizations in terms of partial flag varieties of finite and affine type . Recently, the quantum group associat…
Positivity of Canonical Bases under Comultiplication
Zhaobing Fan, Yiqiang Li
We show the positivity of the canonical basis for a modified quantum affine under the comultiplication. Moreover, we establish the positivity of the i-canonical b…
Geometric Schur Duality of Classical Type, II
Zhaobing Fan, Yiqiang Li
We establish algebraically and geometrically a duality between the Iwahori-Hecke algebra of type D and two new quantum algebras arising from the geometry of N-step isotropic flag v…
An identification of Lusztig's modified forms of quantum algebras and their analogues
Zhaobing Fan, Yiqiang Li
We introduce a multi-parameter twisted Hopf algebra associated with a root datum and show that its modified form is isomorphic to Lusztig's modified quantum algebra under certain r…
Quantum Supergroups III. Twistors
Sean Clark, Zhaobing Fan, Yiqiang Li +1
We establish direct connections at several levels between quantum groups and supergroups associated to bar-consistent super Cartan datum by constructing an automorphism (called twi…
A geometric setting for quantum osp(1|2)
Zhaobing Fan, Yiqiang Li
A geometric categorification is given for arbitrary-large-finite-dimensional quotients of quantum osp(1|2) and the tensor product of its simple modules. The modified quantum osp(1|…
Two-parameter quantum algebras, canonical bases and categorifications
Zhaobing Fan, Yiqiang Li
A theory of canonical basis for a two-parameter quantum algebra is developed in parallel with the one in one-parameter case. A geometric construction of the negative part of a two-…
Geometric approach to Hall algebra of representations of Quivers over local ring
Zhaobing Fan
By using perverse sheaves on representation spaces of quivers over and jet schemes over flag varieties, we construct a geometric composition algebra under…